Perhaps it is the suggestive way in which Christine Lagarde talks of the need for a “harmonised approach to bank recapitalisation”, or how she makes an appeal for “effective fiscal disciplinary standards” sound like a summons to le boudoir.

Like many strong men before him, the BBC’s business editor, Robert Peston, has fallen under the spell of the silvery-coiffed head of the International Monetary Fund, the clatter of whose heels echoes through the corridors of global power like an excited heartbeat. Poor Pesto’s attempts last week to interest his listeners in the IMF’s updated guidance that “the path of consolidation should be in the context of a multi-year plan focused on further reducing the UK’s large structural fiscal deficit” came to an unscripted halt as soon as Mme Lagarde’s name was mentioned.

“She is one of the most charming politicians in the world,” he sighed, attempting to add that “in her silken way, she…”, before Eddie Mair, hosting Radio 4’s PM programme, interrupted to ask: “Are you smitten?”

“I have to say, I’ve met her a few times,” the Balliol College man explained, “and she’s a very seductive politician. Let’s put it that way.” Urged by Mair to return to the subject, he spluttered: “Desperately trying to get back to the matter in hand… No, she, er, said… I’ve completely lost my place, I need a glass of water, and, you know…”

Unrequited as it is doubtless doomed to remain, Peston’s crush possesses a certain poignant plausibility. Along with his sharp brain, the BBC man has the gerbil-like manner of the frantic-to-please school prefect, and Mme Lagarde the coolly sexy calm of the senior economics mistress. “Come to my study after class,” she might purr, and the panting Pesto would be there, eyes crossed and knees knocking, only to be tossed a heap of course notes on labour market intervention strategy.

That Mme Lagarde’s cane now swishes through the fetid air of international finance only adds to her exquisitely French allure. For all that silkiness, a frisson of menace runs through her pronouncements, most recently last week when she showed what looked like a stern face to the plight of the Greeks. Wasn’t she moved by stories of children going without medical care, the 56-year-old mother-of-two was asked. “Do you know what,” she replied, “as far as Athens is concerned, I also think about all those people who are trying to escape tax all the time.” Asked how the Greeks could help themselves, she responded: “By all paying their tax.”

Perhaps distorted by desire, Pesto’s panegyric was wrong in one important respect: Mme Lagarde is not a politician. Admittedly, she served as a cabinet minister for five years, mostly under former president Nicolas Sarkozy, but she has never stood for election and she neither belongs to nor admires the French political class of over-educated administrators and functionaries who run things across the Channel.

Her approach is far more American – shaped by her many years as a high-powered business lawyer with Baker & McKenzie, the giant, Chicago-based international law firm. Her English is near-perfect, but remains foreign enough to have the kind of orphan charm of Jean Seberg’s French in Breathless.

Her enthusiasm for the American way sometimes makes her difficult for the French to admire. Even if, to put it awkwardly, they admire the admiration she gets elsewhere. French women have traditionally had a dismal time in politics. Even today, the Assemblée Nationale has only around 100 women MPs out of a total of 577, making it 74th in the global table of female political representation, behind even Afghanistan. Many voters still think warily back to the calamitous time of Edith Cresson – the country’s first and only female prime minister – who managed to achieve a surreal disapproval rating of 89 per cent before being sacked.

Historians have struggled to explain why a country so socially progressive in other ways has such difficulty in accepting the notion of powerful women. “I must remark on a particular effect of the Revolution,” wrote Arthur Young, the celebrated English chronicler of revolutionary times. “Namely that that enormous power of the female sex has been lessened, and nearly annihilated. Before, women were involved in everything and governed everything, and now their reign is over.”

Mme Lagarde took a different route to the top. She was born Christine Lallouette in Paris to a university professor father and a schoolteacher mother, who shared an unfashionable attachment to Anglo-Saxon culture. They encouraged their daughter to read the great works of English literature and to admire Jefferson and Lincoln, although it took a while for the effects to kick in. The young Christine – a strapping, square-shouldered fille of nearly six foot – was more interested in sport and as a teenager landed a place in the French synchronised swimming team.

At 18, she won a scholarship to study in the US. Ever since, she has worked ferociously hard, against heavy odds, and at some personal cost, to become a success. Her first marriage, in 1982, to a financial analyst called Wilfred Lagarde, produced two sons, but seems to have ended badly a decade later, for all mention of Wilfred has been expunged from her biographies. She then married Eachran Gilmour, a British businessman, of whom even less is known, and is now being romanced by glossy-haired Corsican entrepreneur Xavier Giocanti, with whom she goes scuba diving in the Mediterranean.

Pesto, too, is spoken for – as the husband of writer Siân Busby and father of two sons. But could it ever have worked? Ms Lagarde is a teetotal vegan who heads to the gym each morning, cycles 20 miles at a stretch, swims as often as possible, and practically pulses with the thrill of power. “Success is never complete,” she recently told a French newspaper. “It’s an endless combat. Each morning one must put one’s capacities to the test.”

This is the woman who holds the world economy in her hands. Peston’s big moment was revealing that Northern Rock had run out of money. He’s surely safer staying in Broadcasting House.